The region between two concentric spheres of radii ‘a’ and ‘b’, respectively (see figure), has volume charge density ρ = A/r , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant is:

A long cylindrical shell carries positive surface charge  in the upper half and negative surface charge  in the lower half. The electric field lines around the cylinder will look like figure given in: (figures are schematic and not drawn to scale)

Two charges, each equal to q, are kept at x = −a and x = a on the x-axis. A particle of mass m and charge q_o =-q/2 is placed at the origin. If charge q_o is given a small displacement (y<< a) along the y-axis, the net force acting on the particle is proportional to

• y

• -y

• 1/y

• 1/y

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is

This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.
An insulating solid sphere of radius R has a uniformly positive charge density ρ. As a result of this uniform charge distribution, there is a finite value of the electric potential at the centre of the sphere, at the
surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.

Statement 1: When a charge q is taken from the centre to the surface of the sphere, its potential energy changes by qρ/3ε_o
Statement 2: The electric field at a distance r(r < R) from the centre of the sphere is  ρr/3ε_o

• Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.

• Statement 1 is true, Statement 2 is false

• Statement 1 is false, Statement 2 is true

• Statement 1 is false, Statement 2 is true

In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above will be

7.

Let there be a spherically symmetric charge distribution with charge density varying as   upto r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r ( r < R) from the origin is given by

• 
• 
• 
• 

A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0 ≤ r< ∞ , where r is the distance from the centre of the shell? 

Charges are placed on the vertices of a square as shown. Let E be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then

•  remains unchanged, V changes 

• Both  and V change

•  and V remain unchanged
•  and V remain unchanged

A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields , with a velocity perpendicular to both  , and comes out without any change in magnitude or direction of  .Then